Even though the true structure of ozone is a resonance hybrid where both O-O bond lengths are equal, the total count of localized $\sigma$ and $\pi$ bonds in its valid Lewis representations remains 2 $\sigma$ bonds and 1 $\pi$ bond.
Step 1: Draw ozone. Ozone, $O_3$, has a central oxygen joined to two end oxygens. The shape is bent because of a lone pair on the middle atom.
Step 2: Identify the two bonds. In the Lewis picture the centre oxygen forms one single bond to one end atom and one double bond to the other end atom.
Step 3: Count sigma and pi. A single bond is one sigma. A double bond is one sigma plus one pi. Adding up: \[ \sigma = 1 + 1 = 2, \quad \pi = 1 \]
Step 4: Final count. So ozone has 2 sigma bonds and 1 pi bond. \[ \boxed{2\ \sigma \text{ and } 1\ \pi \text{ bonds}} \]